Question

What percent of the drama club members enrolled at a certain school are female students?
(1) Of the female students enrolled at the school, 40 percent are members of the drama club.
(2) Of the male students enrolled at the school, 25 percent are members of the drama club.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is E Statements (1) and (2) together are not sufficient.

Arithmetic Percents

Determine what percent of drama club members are female.

(1) Knowing that 40 percent of the females enrolled at the school are in the drama club provides no information about the male/ female breakdown of the drama club; NOT sufficient.

(2) Knowing that 25 percent of the males enrolled at the school are in the drama club provides no information about the male/ female breakdown of the drama club; NOT sufficient.

Taking (1) and (2) together does not give enough information to determine what percent of drama club members are female. For example, if the school has 100 female students and 100 male students, then the drama club would have $0.40\left(100\right)+0.25\left(100\right)=40+25=65$ members, $\frac{40}{65}\approx 62$ percent of whom are female. On the other hand, if the school had 40 female students and 160 male students, the drama club would have $0.40\left(40\right)+0.25\left(160\right)=16+40=56$ members, $\frac{16}{56}\approx 29$ percent of whom are female.

The correct answer is E; both statements together are still not sufficient.